I would like to test if the issue persists with disabled qname
minimization, but it seems to be no configurale option.

There's policy.FLAGS({'NO_MINIMIZE'}) action, and you can use on chosen requests, like other policy actions.  Docs:
https://knot-resolver.readthedocs.io/en/latest/modules-policy.html#policy.FLAGS

Example:

policy.add(policy.suffix(policy.FLAGS({'NO_MINIMIZE'}), policy.todnames({'example.net'})))

--Vladimir